Closure to “Discussion of ‘Fluid Film Dynamic Coefficients in Mechanical Face Seals’” (1983, ASME J. Lubr. Technol., 105, p. 503)

1983 ◽  
Vol 105 (3) ◽  
pp. 503-503
Author(s):  
I. Green ◽  
I. Etsion
Keyword(s):  
Fluid Film ◽  
Dynamic Coefficients ◽  
Face Seals

scholarly journals Fluid Film Dynamic Coefficients in Mechanical Face Seals

1983 ◽  
Vol 105 (2) ◽  
pp. 297-302 ◽  
Author(s):  
I. Green ◽  
I. Etsion
Keyword(s):  
Small Perturbation ◽  
Equilibrium Position ◽  
Degrees Of Freedom ◽  
Fluid Film ◽  
Seal Ring ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Face Seals ◽  
Stiffness And Damping ◽  
Analytical Expressions

The stiffness and damping coefficients of the fluid film in mechanical face seals are calculated for the three major degrees of freedom of the primary seal ring. The calculation is based on small perturbation of the ring from its equilibrium position. Analytical expressions are presented for the various coefficients and a comparison is made with results of accurate but more complex analyses to establish the range of applicability.

scholarly journals The Rotor Dynamic Coefficients of Coned-Face Mechanical Seals With Inward or Outward Flow

1987 ◽  
Vol 109 (1) ◽  
pp. 129-135 ◽  
Author(s):  
I. Green
Keyword(s):  
Fluid Film ◽  
Mechanical Seals ◽  
Dynamic Coefficients ◽  
Face Seals ◽  
Stiffness And Damping ◽  
Rotor Dynamic

The linearized fluid film dynamic coefficients, i.e., stiffness and damping, of flexibly-mounted rotor noncontacting mechanical face seals are found. The coefficients are derived from a previous study where the flexibly mounted element was the stator. The two cases of inward and outward flows, both having converging gaps in the direction of flow, are analyzed for the two mounting configurations, and it is found that the later case possesses higher angular stiffness.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

The Rotor Dynamic Coefficients of Eccentric Mechanical Face Seals

1996 ◽  
Vol 118 (1) ◽  
pp. 215-224 ◽  
Author(s):  
J. Wileman ◽  
I. Green
Keyword(s):  
Degrees Of Freedom ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Shear Stresses ◽  
Dynamic Coefficients ◽  
Angular Deflection ◽  
Face Seals ◽  
Radial Forces ◽  
Rotor Dynamic ◽  
Additional Coupling

The Reynolds equation is extended to include the effects of radial deflection in a seal with two flexibly mounted rotors. The resulting pressures are used to obtain the forces and moments introduced in the axial and angular modes by the inclusion of eccentricity in the analysis. The rotor dynamic coefficients relating the forces and moments in these modes to the axial and angular deflection are shown to be the same as those presented in the literature for the concentric case. Additional coefficients are obtained to express the dependence of these forces and moments upon the radial deflections and velocities. The axial force is shown to be decoupled from both the angular and radial modes, but the angular and radial modes are coupled to one another by the dependence of the tilting moments upon the radial deflections. The shear stresses acting upon the element faces are derived and used to obtain the radial forces acting upon the rotors. These forces are used to obtain rotor dynamic coefficients for the two radial degrees of freedom of each rotor. The additional rotor dynamic coefficients can be used to obtain the additional equations of motion necessary to include the radial degrees of freedom in the dynamic analysis. These coefficients introduce additional coupling between the angular and radial degrees of freedom, but the axial degrees of freedom remain decoupled.

scholarly journals Influence of Thermoelastic Phenomena on the Energy Conservation in Non-Contacting Face Seals

Energies ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 5283
Author(s):  
Slawomir Blasiak
Keyword(s):  
Mathematical Model ◽  
Cross Sections ◽  
Thermal Stresses ◽  
Mechanical Energy ◽  
Fluid Film ◽  
Temperature Fields ◽  
Graphical Form ◽  
Asymmetric Distribution ◽  
Thermal Deformations ◽  
Face Seals

The purpose of this study was to develop a mathematical model for non-contacting face seals to analyze how their performance is affected by thermoelastic phenomena. The model was used to solve thermal conductivity and thermoelasticity problems. The primary goal was to calculate the values of thermal deformations of the sealing rings in a non-contacting face seal with a flexibly mounted rotor (FMR) for a turbomachine. The model assumes the conversion of mechanical energy into heat in the fluid film. The heat flux generated in the fluid film is transferred first to the sealing rings and then to the fluid surrounding them. Asymmetric distribution of temperature within the sealing rings leads to the occurrence of thermal stresses and, consequently, a change in the geometry of the rings. The model is solved analytically. The distributions of temperature fields for the sealing rings in the cross-sections are calculated using the Fourier-Bessel series as a superficial function of two variables (r,z). The thermoelasticity problems described by the Navier equations are solved by applying the Boussinesq harmonic functions and Goodier’s thermoelastic displacement potential function. The proposed method involves solving various theoretical and practical problems of thermoelasticity in FMR-type non-contacting face seals. The solution of the mathematical model was made use of analytical methods, and the most important obtained results are presented in graphical form, such as the temperature distributions and axial thermal distortions in cross-sections of the rings. The calculated thermal deformations of the sealing rings are used to determine the most important seal performance parameters such as the leakage rate and power loss. The article also presents a multi-criteria analysis of seal rings materials and geometry, which makes it easier to choose the type of materials used for the sliding rings.

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